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NABATIYEH, Lebanon — Israeli troops sealed off a Hezbollah stronghold, and warplanes killed six persons in a market city in southern Lebanon today, while Beirut was pounded by new air strikes. Guerrillas fired rockets at northern Israel, killing a girl, as the two-week-old crisis showed no signs of letting up, despite U.S. diplomatic efforts.

At least four heavy blasts were heard in Beirut, the first Israeli strikes in the city in nearly two days. A gray cloud rose from the capital’s southern district, a Hezbollah stronghold that has been bombarded heavily. Nearly daily pounding halted during Secretary of State Condoleezza Rice’s visit Monday.

Al-Jazeera television said 20 Israeli rockets hit the Dahiyah neighborhood.

Outlining the scope of the Israeli campaign for the first time, a senior army commander said Israel would only encircle Lebanese towns and villages near the border and did not plan a deeper push into the country.

“The intention is to deal with the Hezbollah infrastructure that is within reach,” Col. Hemi Livni told Israel Army Radio. He commands troops in the western sector of southern Lebanon. “That means in southern Lebanon, not going beyond that.”

President Bush expressed concern for the civilians killed and harmed by Israeli bombs but stopped short of calling for an immediate cease-fire that might not last.

“I support a sustainable cease-fire that will bring about an end to violence,” Mr. Bush said.

Miss Rice, in Israel on the second leg of a Middle East tour, maintained the Bush administration’s position that a cease-fire must come with conditions that make an enduring peace for the region.

“I have no doubt there are those who wish to strangle a democratic and sovereign Lebanon in its crib,” Miss Rice said before meeting with Israeli Prime Minister Ehud Olmert in Jerusalem. “We, of course, also urgently want to end the violence.”

Mr. Olmert welcomed Miss Rice warmly and vowed that “Israel is determined to carry on this fight against Hezbollah.” He said his government “will not hesitate to take severe measures against those who are aiming thousands of rockets and missiles against innocent civilians for the sole purpose of killing them.”

Miss Rice also met with Palestinian Prime Minister Mahmoud Abbas and told him that while she and other allies are engaged in resolving the situation in Lebanon, the United States has not forgotten the Palestinians’ plight.

At a meeting that included about a dozen U.S. and Palestinian officials but no Hamas representatives, Miss Rice and Mr. Abbas talked about getting additional aid to the debt-laden Palestinian government as well as about the status of an Israeli soldier captured last month by Hamas-linked militants.

Mr. Olmert later said Israel has the “stamina for a long struggle” and is determined to defeat the Islamic militant group.

The violence looked likely to drag on with tough ground fighting as Israeli forces try to move village to village near the border, facing well-armed, determined Islamic militant guerrillas who have been digging in for years.

The United States, which is pushing for the deployment of international and Lebanese troops in southern Lebanon to stop Hezbollah attacks on Israel, has angered many allies with its support of Israel and resistance to calls for an immediate cease-fire to the hostilities, which began with a July 12 Hezbollah attack that killed eight Israeli soldiers and captured two.

Arabs will insist on an immediate cease-fire and for the Lebanese government to take control over the militant Hezbollah at an international meeting to be held in Rome tomorrow, Jordanian Foreign Minister Abdul-Illah al-Khatib said.

Iranian President Mahmoud Ahmadinejad, whose nation is a major backer of Hezbollah and a sworn enemy of Israel, said the fighting could trigger “a hurricane” of broader fighting in the Middle East.

German Defense Minister Franz Josef Jung said a cease-fire must be in place before any international troops are sent to Lebanon. Israel has suggested that it would accept an international force — preferably from NATO — to ensure the peace in southern Lebanon, but Mr. Jung said after meeting his French and Polish counterparts that it was too early to say whether the alliance, or a European Union force, could be put in place.

About 300 Americans and 100 Russians, meanwhile, were feared stranded in the heart of Lebanon’s war zone after a ship evacuating foreign nationals from the area left the hard-hit southern port of Tyre on Monday evening. U.S. officials also said the last scheduled evacuations of Americans from Lebanon would happen tomorrow.